There are six consecutive positive integers in Set \(S.\) What is the value of positive integer \(n?\)

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There are six consecutive positive integers in Set \(S.\) What is the value of positive integer \(n?\)

(1) When each integer in \(S\) is divided by \(n,\) the sum of remainders is \(11.\)
(2) When each integer in \(S\) is divided by \(n,\) the remainders include five different values.

Answer: B

Source: Manhattan GMAT
Source: — Data Sufficiency |